Model-guided Performance Analysis of the Sparse Matrix-Matrix Multiplication

TL;DR

This paper analyzes the performance of sparse matrix-matrix multiplication kernels within the Blaze framework, develops models to estimate maximum performance, and compares implementations with other C++ libraries, demonstrating competitive or superior efficiency.

Contribution

It introduces simple performance models for sparse matrix multiplication and evaluates Blaze's implementations against other libraries, highlighting their efficiency.

Findings

Blaze's sparse matrix multiplication is competitive or faster for most problem sizes.

Performance models effectively estimate achievable maximum performance.

Blaze's implementations outperform other SET libraries in many cases.

Abstract

Achieving high efficiency with numerical kernels for sparse matrices is of utmost importance, since they are part of many simulation codes and tend to use most of the available compute time and resources. In addition, especially in large scale simulation frameworks the readability and ease of use of mathematical expressions are essential components for the continuous maintenance, modification, and extension of software. In this context, the sparse matrix-matrix multiplication is of special interest. In this paper we thoroughly analyze the single-core performance of sparse matrix-matrix multiplication kernels in the Blaze Smart Expression Template (SET) framework. We develop simple models for estimating the achievable maximum performance, and use them to assess the efficiency of our implementations. Additionally, we compare these kernels with several commonly used SET-based C++ libraries, which, just as Blaze, aim at combining the requirements of high performance with an elegant user interface. For the different sparse matrix structures considered here, we show that our implementations are competitive or faster than those of the other SET libraries for most problem sizes on a current Intel multicore processor.